AI helps find tumor growth patterns despite messy sparse data
AI-Assisted Tumor-Growth Law Discovery from Sparse Data: Refitting and LLM-Based Ranking
Machine Learning
Summary
Finding mathematical rules that describe how tumors grow is hard when data is scarce and noisy. The authors study an AI-assisted process combining formula searching, checks for valid math, refitting, and assessments using large language models (LLMs). They find that trying to refit formulas with neural networks can sometimes worsen the fit, while classical curve fitting often helps. Importantly, even formulas that fit the data well and seem reasonable can be wrong, so it's crucial to check both predictive accuracy and mathematical validity.
What this means in practice
- •For medical data teams: Improve tumor growth model selection workflows that combine symbolic regression and traditional fitting methods on limited clinical data.
- •For biomedical engineers: Develop better approaches to validating tumor growth laws by integrating mathematical checks alongside predictive accuracy measures.
Authors
Yitian Lu, Weinan Wang
Abstract
Inferring tumor-growth laws from sparse, noisy observations requires more than accurate curve fitting. We study an AI-assisted workflow involving symbolic regression, mathematical admissibility checks, coefficient refitting, and large language model (LLM) ranking. Synthetic Gompertz data allow trajectory fit, forecasting, and recovery of the governing growth law to be assessed separately. A dense noiseless control recovers the generating family, but sparse noisy sampling frequently leads to alternative forms. Among retained candidates in the tested configurations, physics-informed neural network refitting often increases growth-law error, whereas classical nonlinear least squares usually reduces it. A separate exploratory analysis of archived LLM rankings shows no consistent improvement over selection by training error and identifies errors in mathematical reasoning. Plausible saturation, accurate trajectory fits, and convincing explanations can therefore coexist with incorrect growth laws. Mathematical validity and law recovery require evaluation alongside predictive performance.